Finite Group Databasebeta

← #21461193

Subgroups — #21461193

Order 7808.

238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840780C211yesmaximal, characteristic, complemented
2#16840698C211yesmaximal, characteristic, complemented
3#16840615C212yesmaximal, complemented
4#16840614C212yesmaximal
5#16840297C211yesmaximal, characteristic
6C2×C4×#6923—21no—
7#14519844—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519772—21no—
13#14519765C411yescharacteristic, complemented
14#14519762—21no—
15#14519757C2211yescharacteristic
16#14519752C2211yescharacteristic
17#14519742C411yescharacteristic, complemented
18#14519739—21no—
19#14519739C411yescharacteristic, complemented
20#14519735—21no—
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×D244—21no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61C2311yescharacteristic
30C2×Dic122C2×C411yescharacteristic
31C2×#92420—22no—
32C4×#6923—24no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C411yescharacteristic
36C4⋊C4×C61C2×C411yescharacteristic
37C42×C61C2×C411yescharacteristic
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43C4⋊Dic61—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C22×D61—21no—
50C22×D61C2×D411yescharacteristic
51C2×#6923—24no—
52C2×#6923—42no—
53C2×#6923—42no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63D244—41no—
64D244—42no—
65C4×D61—22no—
66C4×D61—22no—
67C4×D61—41no—
68C4×D61—42no—
69Dic122—41no—
70#92420—42no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C2×D61#13512yes—
78#6923—44no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84Dic61—21no—
85Dic61—21no—
86Dic61—41no—
87Dic61#10412yes—
88#1500—611nomaximal, Sylow
89C2×C61#41011yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61C2×#10411yescharacteristic
92D61—22no—
93D61—81no—
94#529—611no—
95#431—611no—
96#376—611no—
97#328—612no—
98#327—612no—
99C61#150011yescharacteristic, complemented, Sylow
100#126—1221no—
101#125#692311yescharacteristic, complemented
102#124—611no—
103#123—1221no—
104C22⋊Q8—611no—
105#121—611no—
106C4×Q8—611no—
107C4×D4—611no—
108C4×D4—1221no—
109#117—1221no—
110C2×C42—611no—
111C2×C42—1221no—
112C4⋊C8—1221no—
113C22⋊C8—612no—
114C4×C8—1221no—
115#95—612no—
116#95—1221no—
117C2×Q8—611no—
118C2×D4—611no—
119C2×D4—1221no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1221no—
124C22×C4—1222no—
125C2×C8—1222no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4C2×#692311yescharacteristic
131C4⋊C4C2×#692311yescharacteristic
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—1221no—
141C42—1224no—
142C42C2×#692311yescharacteristic
143C23—611no—
144C23—1221no—
145Q8—2441no—
146D4—2441no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1222no—
155C2×C4—1224no—
156C2×C4—1221no—
157C2×C4—2441no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4—2442no—
161C2×C4C22⋊#692311yescharacteristic
162C2×C4C22⋊#692311yescharacteristic
163C2×C4C22×#692311yescharacteristic
164C8—2442no—
165C22—612no—
166C22—1221no—
167C22—1221no—
168C22—2441no—
169C22—2441no—
170C22—2441no—
171C22C2×C22⋊#692311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—612no—
178C4—1221no—
179C4—1221no—
180C4—2444no—
181C4—2441no—
182C2—1222no—
183C2—4881no—
184C2#1684074311yescharacteristic
185C2#1684075211yescharacteristic
186C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1500
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16840780C2semidirect
2. #16840698C2semidirect
3. #16840615C2semidirect
13. #14519765C4semidirect
17. #14519742C4semidirect
19. #14519739C4semidirect
22. #125×C61C4semidirect
99. C61#1500semidirect
101. #125#6923semidirect